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A toric lens is a
lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements ...
with different
optical power In optics, optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the ...
and
focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foc ...
in two orientations perpendicular to each other. One of the lens surfaces is shaped like a "cap" from a
torus In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does n ...
(see figure at right), and the other one is usually
spherical A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ce ...
. Such a lens behaves like a combination of a spherical lens and a
cylindrical lens A cylindrical lens is a lens which focuses light into a line instead of a point, as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it into a line parallel to ...
. Toric lenses are used primarily in
eyeglass Glasses, also known as eyeglasses or spectacles, are vision eyewear, with lenses (clear or tinted) mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms (known as temples ...
es,
contact lens Contact lenses, or simply contacts, are thin lenses placed directly on the surface of the eyes. Contact lenses are ocular prosthetic devices used by over 150 million people worldwide, and they can be worn to correct vision or for cosmeti ...
es and
intraocular lens Intraocular lens (IOL) is a lens (optics), lens implanted in the human eye, eye as part of a treatment for cataracts or myopia. If the natural lens is left in the eye, the IOL is known as Phakic intraocular lens, phakic, otherwise it is a pseudop ...
es to correct
astigmatism Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. This results in distorted or blurred vision at any distance. Other symptoms can include eyestrain, headaches, and trouble driving at n ...
.


Torus

A torus is the surface of revolution resulting when a circle with radius ''r'' rotates around an axis lying within the same plane as the circle, at a distance ''R'' from the circle's centre (see figure at right). If ''R'' > ''r'', a ''ring torus'' is produced. If ''R'' = ''r'', a ''horn torus'' is produced, where the opening is contracted into a single point. ''R'' < ''r'' results in a ''spindle torus'', where only two "dips" remain from the opening; these dips become less deep as ''R'' approaches 0. When ''R'' = 0, the torus degenerates into a
sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...
with radius ''r''.


Radius of curvature and optical power

The greatest radius of curvature of the toric lens surface, , corresponds to the smallest refractive power, ''S'', given by : S = \frac , where ''n'' is the
index of refraction In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
of the lens material. The smallest radius of curvature, ''r'', corresponds to the greatest refractive power, ''s'', given by : s = \frac . Since , . The lens behaves approximately like a combination of a spherical lens with optical power ''s'' and a
cylindrical lens A cylindrical lens is a lens which focuses light into a line instead of a point, as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it into a line parallel to ...
with power . In
ophthalmology Ophthalmology ( ) is a surgical subspecialty within medicine that deals with the diagnosis and treatment of eye disorders. An ophthalmologist is a physician who undergoes subspecialty training in medical and surgical eye care. Following a me ...
and
optometry Optometry is a specialized health care profession that involves examining the eyes and related structures for defects or abnormalities. Optometrists are health care professionals who typically provide comprehensive primary eye care. In the Un ...
, is called the ''cylinder power'' of the lens. Note that both the greatest and the smallest curvature have a ''circular'' shape. Consequently, in contrast with a popular assumption, the toric lens is ''not'' an ellipsoid of revolution.


Light ray and its refractive power

Light ray In optics a ray is an idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation o ...
s within the (''x'',''y'')-plane of the torus (as defined in the figure above) are
refracted In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
according to the greatest radius of curvature, , which means that it has the smallest refractive power, ''S''. Light rays within a plane through the axis of revolution (the ''z'' axis) of the torus are refracted according to the smallest radius of curvature, ''r'', which means that it has the greatest refractive power, ''s''. As a consequence, there are two different refractive powers at orientations perpendicular to each other. At intermediate orientations, the refractive power changes gradually from the greatest to the smallest value, or reverse. This will compensate for the astigmatic aberration of the eye.


Atoric lens

With modern computer-controlled design, grinding and polishing techniques, good vision corrections can be achieved for even wider angles of view by allowing certain deviations from the toric shape. This is called an ''atoric lens'' (literally, non-toric lens).Volk, D.: ''Aspheric Lenses''
, in ''Duane's Ophthalmology'', chapter 50 (Lippinkott, Wilkins & Williams / Wolters-Kluwer Health, Chicago, USA) They are related to toric lenses in the same way that
aspheric lens An aspheric lens or asphere (often labeled ''ASPH'' on eye pieces) is a lens (optics), lens whose surface profiles are not portions of a sphere or Cylinder (geometry), cylinder. In photography, a camera lens, lens assembly that includes an aspheri ...
es are related to spherical lenses.


Notes


References

{{reflist Geometrical optics Corrective lenses